Publication detail

Perturbation of time scale quadratic functionals with variable endpoints

RŮŽIČKOVÁ, V. HILSCHER, R.

English title

Perturbation of time scale quadratic functionals with variable endpoints

Type

Peer-reviewed article not indexed in WoS or Scopus

Language

en

Original abstract

In this paper we establish perturbation results pertaining the nonnegativity and positivity of a time scale quadratic functional $\F_0$ and its perturbations of the form $$ \G(x,u)=\F_0(x,u)+\alpha\,\|x(a)\|^2+\beta\,\|x(b)\|^2, $$ where the endpoints of the functional $\F_0$ are zero while the endpoints of the functional $\G$ can vary. These functionals are closely related to time scale symplectic systems. Moreover, we extend such results to functionals with variable endpoints. The results of this paper generalize perturbation results recently known for the special case of the discrete time, but they are new for the continuous time.

Keywords in English

Quadratic functional, Nonnegativity, Positivity, Time scale, Time scale symplectic system, Linear Hamiltonian system.

Released

2007-12-31

Publisher

Research India Publications

ISSN

0973-5321

Journal

Advances in Dynamical Systems and Applications (ADSA)

Volume

2

Number

2

Pages from–to

207–224

Pages count

18

BIBTEX


@article{BUT44057,
  author="Viera {Štoudková Růžičková} and Roman Šimon {Hilscher}",
  title="Perturbation of time scale quadratic functionals with variable endpoints",
  journal="Advances in Dynamical Systems and Applications (ADSA)",
  year="2007",
  volume="2",
  number="2",
  pages="207--224",
  issn="0973-5321"
}